Coupling a branching process to an infinite dimensional epidemic process

Branching process approximation to the initial stages of an epidemic process has been used since the 1950's as a technique for providing stochastic counterparts to deterministic epidemic threshold theorems. One way of describing the approximation is to construct both branching and epidemic processes on the same probability space, in such a way that their paths coincide for as long as possible. In this paper, it is shown, in the context of a Markovian model of parasitic infection, that coincidence can be achieved with asymptotically high probability until o(N^{2/3}) infections have occurred, where N denotes the total number of hosts.Comment: 16 page

Long-term concentration of measure and cut-off

We present new concentration of measure inequalities for Markov chains that enjoy a contractive property. We apply our discrete-time inequality to the well-studied Bernoulli-Laplace model of diffusion, and give a probabilistic proof of cut-off, recovering the optimal bounds of Diaconis and Shahshahani. We also extend the notion of cut-off to chains with an infinite state space, and illustrate this in a second example, of a two-host model of disease in continuous time.Comment: 36 page

An ethnography of students' extensive use of computers and digital technologies within further education classrooms

This thesis analyses how the extensive use of networked computers, which were the primary classroom learning resource for three Level 3 cohorts of Further Education students, impacted on how the students approached the academic elements of their coursework. Using an ethnographic methodology the students were followed as they progressed over one academic year, to identify how they engaged with their learning and used the technologies over this period. The study of students’ classroom academic and literacy practices when using the new digital technologies of computers and the Internet as resources in post-compulsory education is a relatively neglected area. At a time when there is the continued call for the increased use of these technologies across the curricula, this ethnography offers an insight into students’ responses to the technologies and how these significant educational resources can also divide the classroom into both educational and social-leisure spaces. What became apparent over the year was students’ superficial level of engagement with online research resources and how that information was then processed. Students’ use of software to manipulate digital text bypassed any evidencing of intermediary cognitive processes, therefore at times idea generation, critical development and level of ownership became challenging to identify. Notably, students’ extensive use of computers resulted in their gaze being primarily directed to their computer monitors and despite the sociality amongst students for non-educational activities, both in and out of the classrooms, the benefits of peer discussion and interaction for learning was absent due to this level of academic isolation. Students’ use of the technologies for either educational or social-leisure use was reflective of the learning conditions and what affected their levels of motivation and attention. For a number of students, their excessive use of the classroom computers to access online social-leisure resources came at a cost to their grades and their ambitions for progression had to be reduced. There is no doubting the value of computers and the Internet as classroom learning resources, however, this research identifies that they are certainly not a quick panacea for education. The evidence illustrates that to attain the potential they offer, there needs to be relative adjustments to pedagogy and learning cultures and how students conceptualise the space of computer-resourced classrooms